The sum of two angles is $78^\circ$. Angle 2 is $57^\circ$ smaller than $2$ times angle 1. What are the measures of the two angles in degrees?
Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 78}$ ${y = 2x-57}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${2x-57}$ for $y$ in the first equation. ${x + }{(2x-57)}{= 78}$ Simplify and solve for $x$ $ x+2x - 57 = 78 $ $ 3x-57 = 78 $ $ 3x = 135 $ $ x = \dfrac{135}{3} $ ${x = 45}$ Now that you know ${x = 45}$ , plug it back into $ {y = 2x-57}$ to find $y$ ${y = 2}{(45)}{ - 57}$ $y = 90 - 57$ ${y = 33}$ You can also plug ${x = 45}$ into $ {x+y = 78}$ and get the same answer for $y$ ${(45)}{ + y = 78}$ ${y = 33}$ The measure of angle 1 is $45^\circ$ and the measure of angle 2 is $33^\circ$.